Inferring the background traffic arrival process in the Internet.

Phase transition has been found in many complex interactivity systems. Complex networks are not exception either but there are quite few real systems where we can directly understand the emergence of this nontrivial behavior from the microscopic view. In this paper, we present the emergence of the phase transition between the congested and uncongested phases of a network link. We demonstrate a method to infer the background traffic arrival process, which is one of the key state parameters of the Internet traffic. The traffic arrival process in the Internet has been investigated in several studies, since the recognition of its self-similar nature. The statistical properties of the traffic arrival process are very important since they are fundamental in modeling the dynamical behavior. Here, we demonstrate how the widely used packet train technique can be used to determine the main properties of the traffic arrival process. We show that the packet train dispersion is sensitive to the congestion on the network path. We introduce the packet train stretch as an order parameter to describe the phase transition between the congested and uncongested phases of the bottleneck link in the path. We find that the distribution of the background traffic arrival process can be determined from the average packet train dispersion at the critical point of the system.